# Simulation Study: Data-Driven Material Decomposition in Industrial X-ray Computed Tomography

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## Abstract

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## 1. Introduction

- A fast CT simulation pipeline which is capable of generating thousands of tomograms for real-time training of the data-driven model.
- Quantitative end-to-end material decomposition results of simulated alloys without relying on K-edge absorption and leveraging spatial information.

## 2. Computed Tomography Background

## 3. Related Work

## 4. Methods

#### 4.1. CT Simulation

#### 4.2. Data

#### 4.3. Model and Training

## 5. Results

#### 5.1. Test on Simulated CT Data

#### 5.2. Test on Real CT Data

## 6. Outlook

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**Comparison of spectra and absorption coefficients. $95\%$ of the signal, measured with an energy-integrating detector, originates from the photons in the energy bins shaded below the curve assuming a $0.4\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ CsI scintillator.

**Figure A2.**Comparison of spectra and absorption coefficients. $95\%$ of the signal, measured with an energy-integrating detector, originates from the photons in the energy bins shaded below the curve assuming a $0.4\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ CsI scintillator.

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**Figure 1.**Pipeline overview for training data generation with computing modules in red and data objects in green. A tuple $(x,y)$ consists of a tensor of tomograms x and a tensor of material phantoms y. The spatial dimensionality of x and y is identical, and the tomograms and phantoms are fully registered.

**Figure 2.**Comparison of spectra and absorption coefficients: $95\%$ of the signal, measured with an energy-integrating detector, originates from the photons in the energy bins shaded below the curve assuming a $0.4\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ CsI scintillator.

**Figure 3.**Data tuple used for training with a $80\phantom{\rule{0.166667em}{0ex}}\mathrm{kVp}$ tomogram and a $150\phantom{\rule{0.166667em}{0ex}}\mathrm{kVp}$ tomogram as inputs on the left and ground truth material distributions of magnesium and aluminium on the right. The tomograms share the colour scale on the left side. The material maps share the colour scale on the right side.

**Figure 4.**Model architecture mainly used for this work related to a shallow U-Net. Numbers above tensors indicate the number of features.

**Figure 5.**Qualitative comparison of the model’s prediction (pred) and the ground truth (GT). The input DECT tomograms are in the first column and normalised separately, but the colour scale is shared next to them. The absolute differences between ground truths and predictions are shown in the final column and are in units of density described by the colour scale on the right, which also relates to ground truths and predictions. The amplitude of the difference images is magnified by 10.

**Figure 6.**Pixel-by-pixel comparison of ground truth and prediction for 8000 randomly polled tuples from the test dataset. The colour scale indicates the number of points that fall in a certain bin. The prediction and ground truth are expressed in relative fraction units for a specific pixel and material. For instance, if a pixel consists of 30% magnesium, the corresponding ground truth value will be 0.3.

**Figure 7.**Pixel-by-pixel comparison of ground truth and prediction for a material consisting of Ti and Ti64. The colour scale indicates the number of points that fall in a certain bin. Note the different range described by the colour scale in comparison to Figure 6. The prediction and ground truth are expressed in relative fraction units for a specific pixel and material.

**Figure 8.**Qualitative comparison of the model’s prediction (pred) and the ground truth (GT). The input DECT tomograms are in the first column and normalised separately but share the colour scale next to them. The absolute differences between ground truths and predictions are shown in the final column and are in units of density described by the colour scale on the right, which also relates to ground truths and predictions. The amplitude of the difference images is magnified by 10. Note the lower image resolution compared to Figure 5 due to the high cost of computation and generally slower convergence for this material system.

**Figure 9.**Overview of the 10c euro coin scan. (

**Left**) low-energy tomogram with the cut line. (

**Middle**) low-energy and high-energy tomograms along the cut line. (

**Right**) model’s prediction on copper, residuals and air. The tomograms are normalised against the min-max range from the underlying training dataset. The model output is in units of relative volume fraction. Ideally, $89\%$ copper and $11\%$ residuals are expected homogenically inside the coin.

**Table 1.**Mean $\nu $ and standard deviation $\sigma $ of the model’s residuals for different material combinations. The superscripted dagger

^{†}indicates the usage of higher peak voltages for the X-ray spectra to penetrate the samples sufficiently.

Mg–Al | Al–Fe | Fe–Cu ^{†} | Ti64-AlSi | Ti64-Ti ^{†} | |
---|---|---|---|---|---|

$\nu $/${10}^{-4}$ | −6.2 | 9.00 | 9.56 | −5.5 | 4.8 |

$\sigma $/${10}^{-3}$ | 9.17 | 9.56 | 10.26 | 9.3 | 52.4 |

CT Geometry | Source: low-energy/high-energy | ||

Magnification | 3.5 | Tube voltage | $300\phantom{\rule{0.166667em}{0ex}}\mathrm{kVp}$/$450\phantom{\rule{0.166667em}{0ex}}\mathrm{kVp}$ |

Projections | 1500 full-circle | Tube Current | $2\phantom{\rule{0.166667em}{0ex}}\mathrm{mA}$/$1\phantom{\rule{0.166667em}{0ex}}\mathrm{mA}$ |

Scan time | 8 min | Filter | $1\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ Cu + $1\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ Sn |

Detector | |||

Type | energy-integrating | ||

Scintillator | $400\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}\mathrm{m}$ caesium iodide | ||

Pixel Size | $278\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}\mathrm{m}$ | ||

Number of Channels | (1500, 1500) |

**Table 3.**Mean $\nu $ and standard deviation $\sigma $ of the model’s prediction for each base material in a real CT scan of Nordic gold calculated in the coin. The real copper fraction in Nordic gold is $89\%$, which is around $20\%$ higher than our model predicted. The mean fractions in the table do not sum to $100\%$ since the values shown are rounded.

Copper | Residuals | Air | |
---|---|---|---|

$\nu $/${10}^{-2}$ | 69.8 | 30.2 | 0.1 |

$\sigma $/${10}^{-2}$ | 21.7 | 21.7 | 0.3 |

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**MDPI and ACS Style**

Weiss, M.; Brierley, N.; von Schmid, M.; Meisen, T.
Simulation Study: Data-Driven Material Decomposition in Industrial X-ray Computed Tomography. *NDT* **2024**, *2*, 1-15.
https://doi.org/10.3390/ndt2010001

**AMA Style**

Weiss M, Brierley N, von Schmid M, Meisen T.
Simulation Study: Data-Driven Material Decomposition in Industrial X-ray Computed Tomography. *NDT*. 2024; 2(1):1-15.
https://doi.org/10.3390/ndt2010001

**Chicago/Turabian Style**

Weiss, Moritz, Nick Brierley, Mirko von Schmid, and Tobias Meisen.
2024. "Simulation Study: Data-Driven Material Decomposition in Industrial X-ray Computed Tomography" *NDT* 2, no. 1: 1-15.
https://doi.org/10.3390/ndt2010001